Where is the input box for setting the number of `Vertices` of a circle?
Steps


Press Shift + A and select Circle to add a new circle to the scene.  


After clicking the Circle, the input box of Vertices is now shown in the left hand side menu.






Explanation

The editbox for that only appears directly and automatically after you added the circle to the scene.
If you switch to editmode after that then you can't change it anymore that way.

You'll need to undo the adding, add it again and change the value right away and THEN go into editmode to work on it further.

Alternatively you can just stay in editmode, remove all vertices and add a new circle, it'd be the same in the end.